Policy Inquiry – Policy Inquiry – Lecture 1Lecture 1Common Sense and the Elementary Common Sense and the Elementary Forms of Statistical ReasonForms of Statistical Reason

We rely on crude statistical We rely on crude statistical thinking at all timesthinking at all times

We “count” things all the timeWe “count” things all the time Only difference between how we talk and Only difference between how we talk and

how statisticians “talk” is in how how statisticians “talk” is in how “carefully” we count“carefully” we count 76% of VT students favor faculty evaluations76% of VT students favor faculty evaluations Most of the students favor faculty Most of the students favor faculty

evaluationsevaluations The students at VT favor faculty evaluationsThe students at VT favor faculty evaluations

Common SenseCommon Sense

While people regularly dismiss statistical While people regularly dismiss statistical arguments, they regularly submit to arguments, they regularly submit to “common sense”“common sense”

If we trust common sense, we should If we trust common sense, we should trust statistics moretrust statistics more

Why? Well, how do we create “common Why? Well, how do we create “common sense” – what methods do we use, and sense” – what methods do we use, and are they different from statistics?are they different from statistics?

We depend on typicalityWe depend on typicality

The most important method seems to be The most important method seems to be to arrange things in terms of how typical to arrange things in terms of how typical we think they arewe think they are We do this automatically, without thinking We do this automatically, without thinking

about itabout it We readily talk about We readily talk about averageaverage ability, ability, normalnormal

intelligence, intelligence, typicaltypical appearance, business as appearance, business as usualusual

TaskTask

Draw a “typical building”Draw a “typical building” ShareShare Could we program this?Could we program this?

TypificationTypification

Typification is a necessary component of Typification is a necessary component of human communicationhuman communication

It is a form of logic – or a “logical form”It is a form of logic – or a “logical form” It appears in both ordinary discourse and It appears in both ordinary discourse and

statistical workstatistical work

Assessing TypicalityAssessing Typicality

The way we do it in statistics is basically the The way we do it in statistics is basically the same as how we do it every daysame as how we do it every day Actually, in everyday discourse, we often get much Actually, in everyday discourse, we often get much

fancierfancier

Most prevalent method – look around and Most prevalent method – look around and figure out what is predominantfigure out what is predominant New MPA class mostly male or female?New MPA class mostly male or female? Describe the typical senatorDescribe the typical senator What do statisticians call this kind of typicality?What do statisticians call this kind of typicality?

Typicality cont.Typicality cont.

““We be black and they white. They got things and we We be black and they white. They got things and we ain’t. They do things and we can’t. It’s just like living in ain’t. They do things and we can’t. It’s just like living in jail.”jail.”

Richard Richard Wright, Native SonWright, Native Son

What is Richard Wright telling us? List the typicalitiesWhat is Richard Wright telling us? List the typicalities The point is that through literature Wright is making a The point is that through literature Wright is making a

statistical argumentstatistical argument he’s using a logical form – the idea of typicalityhe’s using a logical form – the idea of typicality

Does this passage still apply today? How can we tell? Does this passage still apply today? How can we tell? Are things different? How much different?Are things different? How much different?

TaskTask

Everybody standup and line up by height Everybody standup and line up by height at the back of the roomat the back of the room

““least-tall” on left, “least-short” on rightleast-tall” on left, “least-short” on right Who’s in the middle?Who’s in the middle? What kind of typicality is this?What kind of typicality is this? Where do we see this type of “average” Where do we see this type of “average”

used the most? Why?used the most? Why?

TaskTask

Measure your headsMeasure your heads Measure you handsMeasure you hands Add all together and divide by number of Add all together and divide by number of

people in the roompeople in the room What type of average is this?What type of average is this? When do we do this kind of averaging? When do we do this kind of averaging?

Why?Why? Keep you measurements!Keep you measurements!

““Typical” Statistical Typical” Statistical AveragesAverages

ModeMode What is there the most of?What is there the most of?

MedianMedian What’s in the middle?What’s in the middle?

MeanMean If you put everything together and then equally If you put everything together and then equally

distributed it, how much would everybody get?distributed it, how much would everybody get?

Other less “typical” (for us!)Other less “typical” (for us!) http://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Average

TaskTask

Write down description of a typical one-person Write down description of a typical one-person bandband The type of musician that performs on street corners The type of musician that performs on street corners

and can play multiple instruments at the same timeand can play multiple instruments at the same time Where did you get this idea?Where did you get this idea? If it were a short Ethiopian woman playing the If it were a short Ethiopian woman playing the

viola and clarinet at the same time, would that viola and clarinet at the same time, would that alter your thinking of the typical one-person alter your thinking of the typical one-person band?band?

What do we call a conceptual average that is What do we call a conceptual average that is hard to break?hard to break?

Why Typify?Why Typify?

So, why do we typify?So, why do we typify? Consider you are about to meet someone for Consider you are about to meet someone for

the first time and you know little about this the first time and you know little about this personperson

If you are wise, you will assume s/he is more or If you are wise, you will assume s/he is more or less a typical person – WHY?less a typical person – WHY?

Answer: it minimizes total sum of errorsAnswer: it minimizes total sum of errors What would happen if we decided that every What would happen if we decided that every

new person we met was a jerk? How much re-new person we met was a jerk? How much re-evaluation would be necessary?evaluation would be necessary?

Folk Terms for Central Folk Terms for Central TendencyTendency

Average, commonplace, consistent, Average, commonplace, consistent, humdrum, conventional, normal, humdrum, conventional, normal, ordinary, standard, stereotypical, popular, ordinary, standard, stereotypical, popular, prevailing, regular, stock, typical, prevailing, regular, stock, typical, unexceptional, uniform, usualunexceptional, uniform, usual

Any time you see one of these words Any time you see one of these words used in spoken or written communication, used in spoken or written communication, a statistical argument is being madea statistical argument is being made

Folk vs. StatisticalFolk vs. Statistical

While people often believe that “folk” While people often believe that “folk” ways of assessing things are “easier” ways of assessing things are “easier” than “statistical” ways, it is most often the than “statistical” ways, it is most often the opposite.opposite.

Consider Richard Wright’s statement Consider Richard Wright’s statement again and the complexities involved in again and the complexities involved in what he is sayingwhat he is saying

The AtypicalThe Atypical

If we are interested in typicalities, we are If we are interested in typicalities, we are automatically interested in differencesautomatically interested in differences

We cannot “compare” without thinking about We cannot “compare” without thinking about differencesdifferences

Even small differences can precipitate fights, Even small differences can precipitate fights, depression, arrogance, humility, etc.depression, arrogance, humility, etc.

In the 80s and 90s, a lot of consideration in In the 80s and 90s, a lot of consideration in organizations about the differences between organizations about the differences between Americans and the JapaneseAmericans and the Japanese

Atypical cont.Atypical cont.

People are neurotically obsessed with People are neurotically obsessed with differencesdifferences

People act on differences all the timePeople act on differences all the time Actual or just believedActual or just believed

How many of you are trying to eat less?How many of you are trying to eat less? Why?Why?

If one neighborhood gets better trash service If one neighborhood gets better trash service than another, does it matter? Why?than another, does it matter? Why?

Concern with the atypical defines much of Concern with the atypical defines much of public administrationpublic administration

Folk terms for AtypicalFolk terms for Atypical

Alien, antithesis, contrast, deviant, Alien, antithesis, contrast, deviant, difference, discrepancy, disparity, difference, discrepancy, disparity, dissimilar, distinct, divergent, diversity, dissimilar, distinct, divergent, diversity, heterogeneity, incomparable, heterogeneity, incomparable, individuality, mismatched, modified, individuality, mismatched, modified, originality, peculiar, special, unequal, originality, peculiar, special, unequal, unlike, variance, variation, unusual, unlike, variance, variation, unusual, strange, etc…strange, etc…

Difference for each Difference for each averageaverage

ModeMode Why do we care about what characteristics the Why do we care about what characteristics the

typical senator has?typical senator has? Why do we care how many men vs. women are in Why do we care how many men vs. women are in

graduate school?graduate school? MedianMedian

Why do we care about median income?Why do we care about median income? (Arithmetic) Mean(Arithmetic) Mean

Why would we care about your head size?Why would we care about your head size? What if IQ was involved?What if IQ was involved?

TaskTask

How atypical are you?How atypical are you? Calculate the difference of your head size Calculate the difference of your head size

from the arithmetic mean of the classfrom the arithmetic mean of the class Who are the ‘deviants’?Who are the ‘deviants’? Where do we set the bars?Where do we set the bars?

All Research is Primarily All Research is Primarily about TWO thingsabout TWO things

AveragesAveragesAnd differences from And differences from the averagethe average

CountingCounting

Students generally think that stats is Students generally think that stats is highly numerical (true)highly numerical (true)

Students generally think that ordinary Students generally think that ordinary conversation is not usually numerical conversation is not usually numerical (false)(false)

Only difference is how conscientious we Only difference is how conscientious we are about our countingare about our counting

Careful CountingCareful Counting

We all count, and we count nearly all the timeWe all count, and we count nearly all the time The last bullet contains some countsThe last bullet contains some counts Everyday conversation is loaded with hyperbole that Everyday conversation is loaded with hyperbole that

results from not counting correctly (sometimes on results from not counting correctly (sometimes on purpose, sometimes not)purpose, sometimes not)

““I never do anything right”I never do anything right” If you count the number of times I do things wrong, it will equal If you count the number of times I do things wrong, it will equal

the number of times I have done anything at allthe number of times I have done anything at all Obviously a bad count, and can have serious emotional Obviously a bad count, and can have serious emotional

consequences for the person who believes itconsequences for the person who believes it

Hyperbole vs. Careful Hyperbole vs. Careful Counting in PACounting in PA

This will be one of the forms of statistical reasoning you This will be one of the forms of statistical reasoning you will deal with the mostwill deal with the most

Just about (a count) every complaint that you will Just about (a count) every complaint that you will receive will include an implicit countreceive will include an implicit count

That count will usually (a count) not be a careful countThat count will usually (a count) not be a careful count ““That bridge construction project is taking forever! Or, too That bridge construction project is taking forever! Or, too

long!”long!” ““We are under-serving our disadvantaged citizens!”We are under-serving our disadvantaged citizens!” ““Our recreation resources are terrible compared to other Our recreation resources are terrible compared to other

towns.”towns.” As a public administrator, you will have to deal with bad As a public administrator, you will have to deal with bad

counting from both public AND your political bosses.counting from both public AND your political bosses.

Folk Modifiers for Folk Modifiers for CountingCounting

ManyMany MuchMuch SomeSome NumerousNumerous A littleA little OftenOften A lotA lot A fewA few PlentyPlenty CommonlyCommonly RarelyRarely

What do we count? What do we count? CategorizationCategorization

The scientist (social or otherwise) is concerned The scientist (social or otherwise) is concerned with categorization more than anything elsewith categorization more than anything else

It drives what gets counted and analyzedIt drives what gets counted and analyzed Statement 1: The estimated average density of Statement 1: The estimated average density of

the known universe is equal to one hydrogen the known universe is equal to one hydrogen atom per ten cubic metersatom per ten cubic meters

Statement 2: The average classroom contains Statement 2: The average classroom contains 20 students20 students

Categorization, cont.Categorization, cont.

First statement has well defined categoriesFirst statement has well defined categories Hydrogen atom – has a well defined and excepted Hydrogen atom – has a well defined and excepted

definition – don’t need to wonder whether it is definition – don’t need to wonder whether it is big/small, rich/poor, sick/healthy, old/young, big/small, rich/poor, sick/healthy, old/young, male/femalemale/female

Second statement is not well definedSecond statement is not well defined Category student offers no clue as to what it is Category student offers no clue as to what it is

referring to – older students, special ed, graduate, referring to – older students, special ed, graduate, grade school?grade school?

Category classroom is equally ambiguous – lecture Category classroom is equally ambiguous – lecture hall at a college or elementary school classroom?hall at a college or elementary school classroom?

TaskTask

Define explicitly college student vs. town Define explicitly college student vs. town resident for a census count of Blacksburgresident for a census count of Blacksburg

Present and defend your categorizationPresent and defend your categorization

ProbabilityProbability

What is “probable” is what is “average”What is “probable” is what is “average” POLICY is passed based on a belief of POLICY is passed based on a belief of

averages!averages! Why should we try to minimize drug use in Why should we try to minimize drug use in

teens?teens? Administrative decisions are made on a Administrative decisions are made on a

belief in averages!belief in averages! Why would a locality send its police officers Why would a locality send its police officers

to training?to training?

TaskTask

Let’s draw a “frequency distribution”Let’s draw a “frequency distribution” Across the bottom, let’s divide head size into 5 Across the bottom, let’s divide head size into 5

categories (smallest to largest)categories (smallest to largest) One by one, read off your head measurementsOne by one, read off your head measurements For each category, draw a box for each head For each category, draw a box for each head

that fits that category, stack them up as you get that fits that category, stack them up as you get more than one for that categorymore than one for that category

Calculate the “probability” of having a head Calculate the “probability” of having a head size in the middle categorysize in the middle category

Probability cont.Probability cont.

Probability is a measure of “how likely” we Probability is a measure of “how likely” we think it is that something is going to happen.think it is that something is going to happen.

We figure this out by comparing to the averageWe figure this out by comparing to the average How sure we are of our estimate depends on How sure we are of our estimate depends on

the “variability” of the data around the the “variability” of the data around the “average”“average”

What is we all had the same head size?What is we all had the same head size?

RelationshipsRelationships

The human mind is not content with knowing averages and The human mind is not content with knowing averages and atypicalitiesatypicalities

It also wants to find patterns or relationships – knowing these It also wants to find patterns or relationships – knowing these relationships makes life much easierrelationships makes life much easier

You buy your boyfriend/girlfriend a giftYou buy your boyfriend/girlfriend a gift Why? What relationship do you believe existsWhy? What relationship do you believe exists

You entertain out of town friends by bringing them to an expensive You entertain out of town friends by bringing them to an expensive restaurant you’ve never been torestaurant you’ve never been to Why? What relationships do you believe exist?Why? What relationships do you believe exist?

You help pass legislation that makes any medicine containing You help pass legislation that makes any medicine containing oxycodone be sold behind the counter (you have to ask the oxycodone be sold behind the counter (you have to ask the pharmacist for it)pharmacist for it) Why?Why?

Relationship DefinedRelationship Defined

Where you find X, you Where you find X, you find Yfind Y

Where you don’t find X, Where you don’t find X, you don’t find Yyou don’t find Y This is actually a “positive This is actually a “positive

relationship”relationship” What would a “negative What would a “negative

relationship” be?relationship” be? How about “curvilinear”How about “curvilinear”

Y Not Y Not PresentPresent

Y PresentY Present

X PresentX Present -- ++

X Not X Not PresentPresent

++ --

Relationship LinguisticsRelationship Linguistics

Expressed in many formsExpressed in many forms ““If we cut taxes, people will spend more If we cut taxes, people will spend more

money”money” ““If the road construction contractor finishes If the road construction contractor finishes

on time, he’ll get his bonus”on time, he’ll get his bonus” ““Honor your mother and father.”Honor your mother and father.”

Moral arguments usually have an implicit Moral arguments usually have an implicit statistical argumentstatistical argument

““Eat your spinach!”Eat your spinach!”

TaskTask

Read off your head measurement and Read off your head measurement and hand-spread measurement for me to plothand-spread measurement for me to plot

Do we see a correlation (a relationship)?Do we see a correlation (a relationship)? Do we see causation (a relationship Do we see causation (a relationship

where A actual makes B happen)?where A actual makes B happen)?

Folk Terms for Folk Terms for RelationshipsRelationships

Affiliation, affinity, agreement, Affiliation, affinity, agreement, association, belonging to, comparable, association, belonging to, comparable, connection, contingency, dependence, connection, contingency, dependence, effect, grouping, interdependence, effect, grouping, interdependence, interrelationship, pattern, linkage, interrelationship, pattern, linkage, proportionate, etc.proportionate, etc.

SamplingSampling

To find relationships, statisticians “infer” To find relationships, statisticians “infer” from samples of whatever they are from samples of whatever they are looking atlooking at

Tends to give stats a bad name – why? Tends to give stats a bad name – why? Example?Example?

Sampling cont.Sampling cont.

Fact is, “All” human knowledge, in one way or Fact is, “All” human knowledge, in one way or another, is knowledge derived from a sampling another, is knowledge derived from a sampling of the world around usof the world around us

It would be very difficult to function otherwiseIt would be very difficult to function otherwise You’re preparing fettuccini alfredo for a group of You’re preparing fettuccini alfredo for a group of

friends and you sample it to see if it is seasoned friends and you sample it to see if it is seasoned properlyproperly Anyone against sampling would have to eat the entire dish Anyone against sampling would have to eat the entire dish

to make sureto make sure Look out the side window. Is it raining?Look out the side window. Is it raining?

Anyone against sampling would have to check a window Anyone against sampling would have to check a window on each side of the house to make that determinationon each side of the house to make that determination

Folk Sampling Gone BadFolk Sampling Gone Bad

You’re brought up in a middle-class, white, protestant You’re brought up in a middle-class, white, protestant home and you consider people like this as “normal.” home and you consider people like this as “normal.” Others are not normal, and, possibly bad (you saw Others are not normal, and, possibly bad (you saw some bad African Americans on COPs).some bad African Americans on COPs).

You go to a garage and they mess up. You say you will You go to a garage and they mess up. You say you will never return (a generalization about the quality of all never return (a generalization about the quality of all their work)! Turns out its the best garage in town and their work)! Turns out its the best garage in town and only makes one error for every 10,000.only makes one error for every 10,000.

What is wrong with these samples and What is wrong with these samples and generalizations? N!generalizations? N!

Control (Standardization)Control (Standardization)

By a show of hands, how many of you have By a show of hands, how many of you have ever attempted to grow a mustache or beard?ever attempted to grow a mustache or beard?

What percentage of the class is that?What percentage of the class is that? Divide the little number by the big numberDivide the little number by the big number

So, what is our conclusion about the popularity So, what is our conclusion about the popularity of facial hair among men at Virginia Tech?of facial hair among men at Virginia Tech?

Is there a problem with this conclusion? What?Is there a problem with this conclusion? What?

Control cont.Control cont.

We use control and standardization to simplify We use control and standardization to simplify complex matters so that we can make complex matters so that we can make comparisons.comparisons. Would you compare two runners with one running Would you compare two runners with one running

on a 400yd track and the other a 400m track?on a 400yd track and the other a 400m track?

Anytime you hear “Yes, but…” or “Have you Anytime you hear “Yes, but…” or “Have you considered…” you are being asked a question considered…” you are being asked a question about control and standardizationabout control and standardization

Control, cont.Control, cont.

Can you come up with the “Yes, but…”Can you come up with the “Yes, but…” ““They say if you eat less, you lose weight. I’m eating less, but They say if you eat less, you lose weight. I’m eating less, but

I’m not losing weight.”I’m not losing weight.” ““If poor people would just get some ambition, they could have If poor people would just get some ambition, they could have

anything they want. America is a land of equal opportunity for anything they want. America is a land of equal opportunity for all.”all.”

““If we get better gas mileage from our cars, we will be going a If we get better gas mileage from our cars, we will be going a long way toward improving the environment.”long way toward improving the environment.”

““I figure I have a good lawyer in my case because he said he I figure I have a good lawyer in my case because he said he won every trial he was in.”won every trial he was in.”

Is X REALLY related to Y, or is there a third variable, Z, Is X REALLY related to Y, or is there a third variable, Z, that might be influencing the results?that might be influencing the results?

Folk Control PhrasesFolk Control Phrases

““Yes, but have you considered…”Yes, but have you considered…” ““You are leaving something out…”You are leaving something out…” ““If you take so and so into account…”If you take so and so into account…” ““Yes, but that could also be caused by…”Yes, but that could also be caused by…”

ModelModel

When you put together all your supposed When you put together all your supposed relationships with all necessary controls, relationships with all necessary controls, you get a modelyou get a model

There are two “Types of There are two “Types of Models”Models”

What are they?What are they?1.1. Physical – A smaller tangible thing you can Physical – A smaller tangible thing you can

mess withmess with

2.2. Symbolic - Use words, pictures, lines, Symbolic - Use words, pictures, lines, equations, or computer programs to equations, or computer programs to represent elements and illustrate represent elements and illustrate relationshipsrelationships

Folk Terms for Symbolic Folk Terms for Symbolic ModelsModels

Exemplar, archetype, ideal, map, Exemplar, archetype, ideal, map, paradigm, portrayal, presentation, paradigm, portrayal, presentation, stereotype, etc…stereotype, etc…

TaskTask

Write down three questions that you Write down three questions that you would put on a questionnaire if you were would put on a questionnaire if you were tasked with surveying CPAP MPA tasked with surveying CPAP MPA student opinions about the orientation student opinions about the orientation program for incoming students.program for incoming students.

Task time: 5 minutesTask time: 5 minutes

Basic Model ConstructionBasic Model Construction

What am I trying to figure out – what concepts What am I trying to figure out – what concepts am I trying to measure?am I trying to measure?

What do I need to count to help me figure it What do I need to count to help me figure it out?out? What variables could represent the concept?What variables could represent the concept?

What relationship does this thing you’re What relationship does this thing you’re counting have with the concept you’re trying counting have with the concept you’re trying figure out?figure out? ““If class requirements are clear the student will be If class requirements are clear the student will be

happier”happier” What controls might be needed?What controls might be needed?

TaskTask

Now, with the benefit of basic model building, split into Now, with the benefit of basic model building, split into three groupsthree groups Detail your modelDetail your model What concepts are you trying to measure?What concepts are you trying to measure? What are the relationships between your variables and the What are the relationships between your variables and the

concept (positive or negative)?concept (positive or negative)? Should any control variable be used? Should any control variable be used? Now, formulate, as a group, a question that could be asked to Now, formulate, as a group, a question that could be asked to

collect data for each variablecollect data for each variable Task time: 10 minutesTask time: 10 minutes Did your questions change? Why?Did your questions change? Why? One group will be called up to present their model and One group will be called up to present their model and

defend themselves to their colleagues.defend themselves to their colleagues.

Forms of Statistical LogicForms of Statistical Logic

AverageAverage DeviationDeviation Careful CountingCareful Counting ProbabilityProbability RelationshipsRelationships ControlControl ModelModel CategorizationCategorization

AssignmentAssignment

Write 1 paragraph describing, in your own Write 1 paragraph describing, in your own words, each form of statistical logicwords, each form of statistical logic

For each form, find an example in a newspaper For each form, find an example in a newspaper or news magazine, describe it and give your or news magazine, describe it and give your opinion of its veracityopinion of its veracity What statistical argument are they making?What statistical argument are they making? Is there any data/evidence to back up the argument Is there any data/evidence to back up the argument

or are they simple assertions?or are they simple assertions? Are there any “Yes, but…”s that should be Are there any “Yes, but…”s that should be

considered?considered?